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arXiv · 1511.08376

The K-theory of endomorphisms of spaces

Filipp Levikov
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Abstract

We prove a non-linear version of a theorem of Grayson which is an analogue of the Fundamental Theorem of Algebraic $K$-theory and identify the $K$-theory of the endomorphism category over a space $X$ in terms of reduced $K$-theory of a certain localisation of the category of $\NN$-spaces over $X$. In particular we generalise the result of Klein and Williams describing the nil-terms of $A$-theory in terms of $K$-theory of nilpotent endomorphisms.

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Filipp Levikov. 2015-11-26. The K-theory of endomorphisms of spaces. https://arxiv.org/abs/1511.08376

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